A pro-Russian APC moves along a street in Donetsk on Tuesday. Fighting in eastern Ukraine resumed hours after president Petro Poroshenko declared an end to a ceasefire. Photograph: EPA

Kiev forces claimed their first victories in Petro Poroshenko's renewed offensive against pro-Russian rebels in eastern Ukraine on Tuesday, taking back a key border crossing and three villages.

Ukrainian troops hit rebel positions with artillery and air strikes after the president declared an end to the ceasefire on Monday night, according to the defence ministry. But limited progress around rebel strongholds suggested the campaign would be a protracted one despite government forces' new vigour.

Poroshenko congratulated his troops and border guards after they retook the major Dolzhansk border crossing in the Luhansk region, according to his press service. The president had pledged to re-establish control of Ukraine's border with Russia, which Kiev has long complained is a leaky sieve for weapons and men from its larger neighbour.

In a televised address late on Monday night, Poroshenko said he would not extend the ceasefire that both sides have accused each other of violating and promised to "attack and liberate our land" from "terrorists, rebels, looters". The president has been under pressure from officials and from the general population to take more decisive action in eastern Ukraine, with hundreds protesting against the ceasefire outside the presidential office on Sunday.

In remarks to a group of Russian ambassadors on Tuesday, Vladimir Putin condemned Poroshenko's declaration of an end to the ceasefire and new attacks against the rebels.

"Unfortunately, President Poroshenko decided to renew military actions, and we – I mean myself and my colleagues in Europe – couldn't convince him that the road to reliable, stable and long-term peace can't lie through war," the Russian president said.

He also accused the west of wielding Ukraine in a cold war-style policy of containment against Russia.

"We should clearly understand that the events provoked in Ukraine have become the essence of the proverbial politics of containment," he said.

"Let me stress that what has happened in Ukraine is the culmination of negative tendencies in global affairs and they have been accumulating for years," he added.

A declaration agreed to on Monday night by the foreign ministers of Russia, Germany, France and Ukraine had "welcomed Russia's initiative on placing Ukrainian border guards and OSCE observers at three checkpoints on the Russian territory to control the situation on the border", according to the Russian foreign ministry. But the initiative appeared to come too late for Poroshenko, who said in a statement on Tuesday morning that Moscow had not taken "concrete steps for de-escalating the situation, including strengthening controls on the border".

Kiev has previously promised to create a 10km buffer zone around the border.

On Tuesday, rebels apparently remained in control of the other two border crossings they had seized in the Luhansk region last month. On Friday, European leaders had demanded that all three crossings be given over to the government.

Meanwhile, the national guard commander, Stepan Poltorak, announced that government forces had seized a rebel camp in the village of Zakatnoye and taken control of Stary Karavan and Brusovka in another tactical victory. The three small villages lie along a corridor between the rebel strongholds of Luhansk and Slovyansk, which government forces have been shelling for over a month.

Three Ukrainian soldiers were injured taking Zakatnoye, Poltorak said. Oleksiy Dmytrashkovsky, a spokesman for the defence ministry, told the Interfax news agency that one service member had been killed and 17 wounded in the previous 24 hours, and that an Su-25 jet had been hit but made it back to base.

However, Vladimir Nosikov, a squad commander from the Luhansk-based Ghost Battalion which was previously in Seversk, told the Guardian rebels had driven Ukrainian forces out of Zakatnoye and destroyed one fighting vehicle and one tank. Two fighters were wounded, he said.

Reports on the ground around the east suggested a buildup of Ukrainian arms in key spots, as well as continued shelling of rebel strongholds. Government forces also intensely shelled the city of Kramatorsk overnight and throughout the day on Tuesday, according to the rebel commander of the city, Gennady Kim. Photographs published by the government-linked analytical centre InfoResist showed extensive damage to residential buildings there, while others showed a shot-up minibus with a body lying inside. Kim said the driver of the minibus had been killed and three civilians wounded, but said no rebels had been hurt.

He added that additional tanks and other armour had been deployed by government forces there in apparent preparation for an attack. "We have Molotov cocktails and grenade launchers, a few anti-tank weapons, and it will be very effective in urban setting," he said. "If they enter the city, we won't envy them."

In the city of Karlovka outside Donetsk rebels were reportedly holding their position after trading heavy fire with government forces in the early morning. Rebels continued to consolidate their control of Donetsk, storming the interior ministry regional headquarters on Tuesday/yesterday morning. As heavy machine gun fire continued into the afternoon, a fighter at the scene from the Oplot militia denied reports that rebel groups were fighting among themselves, saying they were attempting to root out a group of unknown snipers. The interior ministry said seven police officers were injured when its office was stormed.

According to Kiev-based defence analyst Alexei Melnik, Kiev's strategy hinges on two objectives: Securing the border to prevent further men, weapons and supplies arriving from Russia, and blocking off rebel-held areas to keep the revolt from spreading. The next stage will be "targeted operations" by special forces to assassinate rebel leaders, Melnik predicted.

Even after the active phase of operations ends, "they will need a few years to bring situation to acceptable level" due to the ongoing the information war between Russia and Ukraine and resentment of Kiev among the local population, he said.